Food competition analysis

Author

Max Lindmark

Published

2024-04-12

Load packages

home <- here::here()

library(tidyverse)
library(tidylog)
library(RCurl)
library(sdmTMB)
library(RColorBrewer)
library(devtools)
library(patchwork)
library(ggstats)
library(ggh4x)
library(sdmTMBextra)

# Source map-plot
#source_url("https://raw.githubusercontent.com/maxlindmark/cod-interactions/main/R/functions/map-plot.R")
source(paste0(home, "/R/functions/map-plot.R"))

Read data & prepare data

d <- read_csv(paste0(home, "/data/clean/aggregated_stomach_data.csv")) %>% 
  drop_na(group) %>% 
  drop_na(oxy)

t <- d %>% filter(fle_kg_km2 > 0)
t <- d %>% filter(mcod_kg_km2 > 0)
t <- d %>% filter(scod_kg_km2 > 0)

# Calculate relative prey weights (saduria and benthos)
d <- d %>% 
  rename(oxygen = oxy) %>% 
  mutate(tot_weight = rowSums(select(., ends_with('_tot'))),  
         benthic_weight = amphipoda_tot + bivalvia_tot + gadus_morhua_tot +
           gobiidae_tot + mysidae_tot + non_bio_tot + 
           other_crustacea_tot + other_tot + other_pisces_tot + platichthys_flesus_tot +
           polychaeta_tot + saduria_entomon_tot) %>% 
  rename(saduria_weight = saduria_entomon_tot,
         flounder_density = fle_kg_km2,
         large_cod_density = mcod_kg_km2,
         small_cod_density = scod_kg_km2) %>% 
  mutate(tot_rel_weight = tot_weight / (pred_weight_g - tot_weight), 
         benthic_rel_weight = benthic_weight / (pred_weight_g - tot_weight),
         saduria_rel_weight = saduria_weight / (pred_weight_g - tot_weight)) %>% 
  dplyr::select(-ends_with("_tot")) %>% 
  dplyr::select(-predator_latin_name, date) %>% 
  # Add small constant to large cod density because we want to take the log of it
  mutate(large_cod_density = ifelse(large_cod_density == 0,
                                    min(filter(d, mcod_kg_km2 > 0)$mcod_kg_km2)*0.5,
                                    large_cod_density),
         flounder_density = ifelse(flounder_density == 0,
                                   min(filter(d, fle_kg_km2 > 0)$fle_kg_km2)*0.5,
                                   flounder_density),
         small_cod_density = ifelse(small_cod_density == 0,
                                    min(filter(d, scod_kg_km2 > 0)$scod_kg_km2)*0.5,
                                    small_cod_density)) %>% 
  # scale variables
  mutate(fyear = as.factor(year),
         fquarter = as.factor(quarter),
         fhaul_id = as.factor(haul_id),
         depth_sc = as.numeric(scale(depth)),
         oxygen_sc = as.numeric(scale(oxygen)),
         density_saduria_sc = as.numeric(scale(density_saduria)),
         flounder_density_sc = as.numeric(scale(log(flounder_density))),
         large_cod_density_sc = as.numeric(scale(log(large_cod_density))),
         small_cod_density_sc = as.numeric(scale(log(small_cod_density))))

Quick explore

Correlation between variables

# Plot correlation between variables
d_cor <- d %>%
  dplyr::select("oxygen_sc", "density_saduria_sc", "flounder_density_sc",
                "large_cod_density_sc", "small_cod_density_sc", "depth_sc")

corr <- round(cor(d_cor), 1)

library(ggcorrplot)
ggcorrplot(corr, hc.order = TRUE, type = "lower", lab = TRUE, lab_size = 2.5) +
  theme_classic() + 
  theme(axis.text.x = element_text(angle = 90, vjust = 0.3))

Sample size

d %>%
  group_by(species) %>% 
  summarise(n = n())
group_by: one grouping variable (species)
summarise: now 2 rows and 2 columns, ungrouped
# A tibble: 2 × 2
  species      n
  <chr>    <int>
1 Cod       5103
2 Flounder  3851
d %>%
  group_by(species, quarter) %>% 
  summarise(n = n())
group_by: 2 grouping variables (species, quarter)
summarise: now 4 rows and 3 columns, one group variable remaining (species)
# A tibble: 4 × 3
# Groups:   species [2]
  species  quarter     n
  <chr>      <dbl> <int>
1 Cod            1  2906
2 Cod            4  2197
3 Flounder       1  2081
4 Flounder       4  1770

Fit models

Groups are: small cod, large cod and flounder. Response variables are: saduria_rel_weight, benthic_rel_weight or total weight. The latter is only for adult cod, because essentially all prey are benthic for small cod and flounder.

Model random effect structure is selected with AIC (see script 02-)

# This is the reason we don't do total weight for flounder and small cod
d %>%
  filter(tot_rel_weight > 0) %>% 
  group_by(group) %>% 
  mutate(ben_prop = benthic_rel_weight / tot_rel_weight) %>% 
  summarise(mean_ben_prop = mean(ben_prop))
# A tibble: 3 × 2
  group     mean_ben_prop
  <chr>             <dbl>
1 flounder          0.978
2 large cod         0.592
3 small cod         0.956

Covariates are: ~ 0 + fyear + fquarter + depth_sc + spatial + spatiotemporal random fields + density covariates. For saduria, we use saduria also in interaction with cod and flounder. For cod we use small cod because large and small cod are very correlated. For benthic and total prey, we instead use oxygen, more as a proxy, as the interaction variable

Main models

pred_flounder_sad <- list()
pred_flounder_ben <- list()
pred_cod_sad <- list()
pred_cod_ben <- list()
coef_sad <- list()
coef_ben <- list()
res_sad <- list()
res_ben <- list()
random_sad <- list()
random_ben <- list()
range_sad <- list()
range_ben <- list()

for(i in unique(d$group)) {
  
  dd <- filter(d, group == i)
  
  mesh <- make_mesh(dd,
                    xy_cols = c("X", "Y"),
                    cutoff = 5)

  ggplot() +
    inlabru::gg(mesh$mesh) +
    coord_fixed() +
    geom_point(aes(X, Y), data = dd, alpha = 0.2, size = 0.5) +
    annotate("text", -Inf, Inf, label = paste("n knots =", mesh$mesh$n), hjust = -0.3, vjust = 3) + 
    labs(x = "Easting (km)", y = "Northing (km)")
  
  ggsave(paste0(home, "/figures/supp/mesh_", i, ".pdf"), width = 17, height = 17, units = "cm")
  
  
  # Saduria model
  
  m_sad <- sdmTMB(saduria_rel_weight ~ 0 + fyear + fquarter + depth_sc + oxygen_sc + 
                    small_cod_density_sc*density_saduria_sc + 
                    flounder_density_sc*density_saduria_sc,
                  data = dd,
                  mesh = mesh,
                  family = tweedie(),
                  spatiotemporal = "IID", 
                  spatial = "on",
                  time = "year")
  print(i)
  sanity(m_sad)
  print(m_sad)
  
  
  # Benthic model
  
    if(unique(dd$group) %in% c("large cod", "small cod")) {
      
      
      m_ben <- sdmTMB(benthic_rel_weight ~ 0 + fyear + fquarter + depth_sc + 
                        small_cod_density_sc*oxygen_sc + flounder_density_sc*oxygen_sc,
                      data = dd,
                      mesh = mesh,
                      family = tweedie(),
                      spatiotemporal = "IID", 
                      spatial = "off", 
                      time = "year")
      print(i)
      sanity(m_ben)
      print(m_ben)
      
    } else {
      
      m_ben <- sdmTMB(benthic_rel_weight ~ 0 + fyear + fquarter + depth_sc + 
                        small_cod_density_sc*oxygen_sc + flounder_density_sc*oxygen_sc,
                      data = dd,
                      mesh = mesh,
                      family = tweedie(),
                      spatiotemporal = "IID", 
                      spatial = "on",
                      time = "year")
      print(i)
      sanity(m_ben)
      print(m_ben)
      
    }
       
   
  # Spatial and spatiotemporal random effects
  d_haul <- dd %>%
    distinct(haul_id, .keep_all = TRUE)

  preds_sad <- predict(m_sad, newdata = d_haul)
  preds_ben <- predict(m_ben, newdata = d_haul)

  random_sad[[i]] <- preds_sad
  random_ben[[i]] <- preds_ben

  # Residuals
  samps <- sdmTMBextra::predict_mle_mcmc(m_sad, mcmc_iter = 401, mcmc_warmup = 400)
  mcmc_res <- residuals(m_sad, type = "mle-mcmc", mcmc_samples = samps)
  dd$res <- as.vector(mcmc_res)

  res_sad[[i]] <- dd

  samps <- sdmTMBextra::predict_mle_mcmc(m_ben, mcmc_iter = 401, mcmc_warmup = 400)
  mcmc_res <- residuals(m_ben, type = "mle-mcmc", mcmc_samples = samps)
  dd$res <- as.vector(mcmc_res)

  res_ben[[i]] <- dd


  # Ranges
  range_sad[[i]] <- tidy(m_sad, effects = "ran_pars") %>% filter(term == "range") %>% mutate(group = i, model = "saduria")
  range_ben[[i]] <- tidy(m_ben, effects = "ran_pars") %>% filter(term == "range") %>% mutate(group = i, model = "benthos")


  # Conditional effects: flounder
  nd_flounder <- data.frame(expand_grid(
    density_saduria_sc = c(quantile(d$density_saduria_sc, probs = 0.05),
                           mean(d$density_saduria_sc),
                           quantile(d$density_saduria_sc, probs = 0.95)),
    flounder_density_sc = seq(quantile(dd$flounder_density_sc, probs = 0.05),
                              quantile(dd$flounder_density_sc, probs = 0.95),
                              length.out = 50))) %>%
    mutate(year = 2020,
           fyear = as.factor(2020),
           fquarter = as.factor(1),
           oxygen_sc = 0,
           depth_sc = 0,
           small_cod_density_sc = 0)

  preds_flounder_sad <- predict(m_sad, newdata = nd_flounder, re_form = NA, re_form_iid = NA, se_fit = TRUE)
  preds_flounder_ben <- predict(m_ben, newdata = nd_flounder, re_form = NA, re_form_iid = NA, se_fit = TRUE)

  pred_flounder_sad[[i]] <- preds_flounder_sad %>% mutate(group = i, xvar = "flounder")
  pred_flounder_ben[[i]] <- preds_flounder_ben %>% mutate(group = i, xvar = "flounder")

  # Conditional effects: cod
  nd_cod <- data.frame(expand_grid(
    density_saduria_sc = c(quantile(d$density_saduria_sc, probs = 0.05),
                           quantile(d$density_saduria_sc, probs = 0.95)),
    small_cod_density_sc = seq(quantile(dd$small_cod_density_sc, probs = 0.05),
                               quantile(dd$small_cod_density_sc, probs = 0.95),
                               length.out = 50))) %>%
    mutate(year = 2020,
           fyear = as.factor(2020),
           fquarter = as.factor(1),
           oxygen_sc = 0,
           depth_sc = 0,
           flounder_density_sc = 0) #

  preds_cod_sad <- predict(m_sad, newdata = nd_cod, re_form = NA, re_form_iid = NA, se_fit = TRUE)
  preds_cod_ben <- predict(m_ben, newdata = nd_cod, re_form = NA, re_form_iid = NA, se_fit = TRUE)

  pred_cod_sad[[i]] <- preds_cod_sad %>% mutate(group = i, xvar = "cod")
  pred_cod_ben[[i]] <- preds_cod_ben %>% mutate(group = i, xvar = "cod")

  # Coefficients
  coefs_sad <- bind_rows(tidy(m_sad, effects = "fixed", conf.int = TRUE)) %>%
    mutate(species = "Cod (m)",
           response = "Saduria",
           sig = ifelse(estimate > 0 & conf.low > 0, "Y", "N"),
           sig = ifelse(estimate < 0 & conf.high < 0, "Y", sig))

  coefs_ben <- bind_rows(tidy(m_ben, effects = "fixed", conf.int = TRUE)) %>%
    mutate(species = "Cod (m)",
           response = "Saduria",
           sig = ifelse(estimate > 0 & conf.low > 0, "Y", "N"),
           sig = ifelse(estimate < 0 & conf.high < 0, "Y", sig))

  coef_sad[[i]] <- coefs_sad %>% mutate(group = i)
  coef_ben[[i]] <- coefs_ben %>% mutate(group = i)

}
filter: removed 5,698 rows (64%), 3,256 rows remaining
Loading required namespace: INLA
[1] "large cod"
✔ Non-linear minimizer suggests successful convergence
✔ Hessian matrix is positive definite
✔ No extreme or very small eigenvalues detected
✔ No gradients with respect to fixed effects are >= 0.001
✔ No fixed-effect standard errors are NA
✔ No standard errors look unreasonably large
✔ No sigma parameters are < 0.01
✔ No sigma parameters are > 100
✔ Range parameter doesn't look unreasonably large
Spatiotemporal model fit by ML ['sdmTMB']
Formula: saduria_rel_weight ~ 0 + fyear + fquarter + depth_sc + oxygen_sc + 
 Formula:     small_cod_density_sc * density_saduria_sc + flounder_density_sc * 
 Formula:     density_saduria_sc
Mesh: mesh (isotropic covariance)
Time column: year
Data: dd
Family: tweedie(link = 'log')
 
                                        coef.est coef.se
fyear2015                                  -8.63    0.93
fyear2016                                 -10.67    0.88
fyear2017                                 -10.92    0.81
fyear2018                                 -10.00    0.88
fyear2019                                 -11.32    1.08
fyear2020                                 -10.27    0.76
fyear2021                                 -10.58    0.79
fyear2022                                 -11.35    0.89
fquarter4                                  -0.69    0.32
depth_sc                                   -1.09    0.28
oxygen_sc                                   0.05    0.24
small_cod_density_sc                        0.29    0.24
density_saduria_sc                          0.43    0.26
flounder_density_sc                        -0.62    0.20
small_cod_density_sc:density_saduria_sc     0.09    0.20
density_saduria_sc:flounder_density_sc      0.07    0.14

Dispersion parameter: 0.13
Tweedie p: 1.47
Matérn range: 34.13
Spatial SD: 2.11
Spatiotemporal IID SD: 1.74
ML criterion at convergence: -731.195

See ?tidy.sdmTMB to extract these values as a data frame.
[1] "large cod"
✔ Non-linear minimizer suggests successful convergence
✔ Hessian matrix is positive definite
✔ No extreme or very small eigenvalues detected
✔ No gradients with respect to fixed effects are >= 0.001
✔ No fixed-effect standard errors are NA
✔ No standard errors look unreasonably large
✔ No sigma parameters are < 0.01
✔ No sigma parameters are > 100
✔ Range parameter doesn't look unreasonably large
Spatiotemporal model fit by ML ['sdmTMB']
Formula: benthic_rel_weight ~ 0 + fyear + fquarter + depth_sc + small_cod_density_sc * 
 Formula:     oxygen_sc + flounder_density_sc * oxygen_sc
Mesh: mesh (isotropic covariance)
Time column: year
Data: dd
Family: tweedie(link = 'log')
 
                               coef.est coef.se
fyear2015                         -6.59    0.29
fyear2016                         -6.48    0.22
fyear2017                         -6.72    0.19
fyear2018                         -6.56    0.22
fyear2019                         -7.51    0.30
fyear2020                         -6.71    0.18
fyear2021                         -6.54    0.17
fyear2022                         -6.79    0.21
fquarter4                          0.83    0.12
depth_sc                          -0.24    0.07
small_cod_density_sc              -0.09    0.06
oxygen_sc                          0.21    0.07
flounder_density_sc                0.04    0.06
small_cod_density_sc:oxygen_sc     0.00    0.04
oxygen_sc:flounder_density_sc      0.04    0.04

Dispersion parameter: 0.27
Tweedie p: 1.63
Matérn range: 9.20
Spatiotemporal IID SD: 1.34
ML criterion at convergence: -7191.001

See ?tidy.sdmTMB to extract these values as a data frame.
distinct: removed 2,968 rows (91%), 288 rows remaining

SAMPLING FOR MODEL 'tmb_generic' NOW (CHAIN 1).
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SAMPLING FOR MODEL 'tmb_generic' NOW (CHAIN 1).
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        new variable 'model' (character) with one unique value and 0% NA
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mutate: new variable 'group' (character) with one unique value and 0% NA
        new variable 'model' (character) with one unique value and 0% NA
mutate: new variable 'year' (double) with one unique value and 0% NA
        new variable 'fyear' (factor) with one unique value and 0% NA
        new variable 'fquarter' (factor) with one unique value and 0% NA
        new variable 'oxygen_sc' (double) with one unique value and 0% NA
        new variable 'depth_sc' (double) with one unique value and 0% NA
        new variable 'small_cod_density_sc' (double) with one unique value and 0% NA
mutate: new variable 'group' (character) with one unique value and 0% NA
        new variable 'xvar' (character) with one unique value and 0% NA
mutate: new variable 'group' (character) with one unique value and 0% NA
        new variable 'xvar' (character) with one unique value and 0% NA
mutate: new variable 'year' (double) with one unique value and 0% NA
        new variable 'fyear' (factor) with one unique value and 0% NA
        new variable 'fquarter' (factor) with one unique value and 0% NA
        new variable 'oxygen_sc' (double) with one unique value and 0% NA
        new variable 'depth_sc' (double) with one unique value and 0% NA
        new variable 'flounder_density_sc' (double) with one unique value and 0% NA
mutate: new variable 'group' (character) with one unique value and 0% NA
        new variable 'xvar' (character) with one unique value and 0% NA
mutate: new variable 'group' (character) with one unique value and 0% NA
        new variable 'xvar' (character) with one unique value and 0% NA
mutate: new variable 'species' (character) with one unique value and 0% NA
        new variable 'response' (character) with one unique value and 0% NA
        new variable 'sig' (character) with 2 unique values and 0% NA
mutate: new variable 'species' (character) with one unique value and 0% NA
        new variable 'response' (character) with one unique value and 0% NA
        new variable 'sig' (character) with 2 unique values and 0% NA
mutate: new variable 'group' (character) with one unique value and 0% NA
mutate: new variable 'group' (character) with one unique value and 0% NA
filter: removed 7,107 rows (79%), 1,847 rows remaining
[1] "small cod"
✔ Non-linear minimizer suggests successful convergence
✔ Hessian matrix is positive definite
✔ No extreme or very small eigenvalues detected
✔ No gradients with respect to fixed effects are >= 0.001
✔ No fixed-effect standard errors are NA
✔ No standard errors look unreasonably large
✔ No sigma parameters are < 0.01
✔ No sigma parameters are > 100
✔ Range parameter doesn't look unreasonably large
Spatiotemporal model fit by ML ['sdmTMB']
Formula: saduria_rel_weight ~ 0 + fyear + fquarter + depth_sc + oxygen_sc + 
 Formula:     small_cod_density_sc * density_saduria_sc + flounder_density_sc * 
 Formula:     density_saduria_sc
Mesh: mesh (isotropic covariance)
Time column: year
Data: dd
Family: tweedie(link = 'log')
 
                                        coef.est coef.se
fyear2015                                  -8.73    1.10
fyear2016                                  -9.22    1.04
fyear2017                                  -9.89    0.99
fyear2018                                  -9.34    1.16
fyear2019                                  -8.25    1.15
fyear2020                                  -9.10    0.97
fyear2021                                  -9.70    0.96
fyear2022                                  -9.45    1.00
fquarter4                                  -1.47    0.36
depth_sc                                   -0.98    0.30
oxygen_sc                                  -0.40    0.25
small_cod_density_sc                        0.44    0.39
density_saduria_sc                          0.58    0.25
flounder_density_sc                        -0.56    0.20
small_cod_density_sc:density_saduria_sc     0.30    0.30
density_saduria_sc:flounder_density_sc      0.03    0.13

Dispersion parameter: 0.18
Tweedie p: 1.50
Matérn range: 65.62
Spatial SD: 2.40
Spatiotemporal IID SD: 1.27
ML criterion at convergence: -599.723

See ?tidy.sdmTMB to extract these values as a data frame.
[1] "small cod"
✔ Non-linear minimizer suggests successful convergence
✔ Hessian matrix is positive definite
✔ No extreme or very small eigenvalues detected
✔ No gradients with respect to fixed effects are >= 0.001
✔ No fixed-effect standard errors are NA
✔ No standard errors look unreasonably large
✔ No sigma parameters are < 0.01
✔ No sigma parameters are > 100
✔ Range parameter doesn't look unreasonably large
Spatiotemporal model fit by ML ['sdmTMB']
Formula: benthic_rel_weight ~ 0 + fyear + fquarter + depth_sc + small_cod_density_sc * 
 Formula:     oxygen_sc + flounder_density_sc * oxygen_sc
Mesh: mesh (isotropic covariance)
Time column: year
Data: dd
Family: tweedie(link = 'log')
 
                               coef.est coef.se
fyear2015                         -6.01    0.31
fyear2016                         -5.82    0.23
fyear2017                         -5.78    0.19
fyear2018                         -5.76    0.23
fyear2019                         -6.34    0.31
fyear2020                         -5.74    0.18
fyear2021                         -5.98    0.17
fyear2022                         -5.83    0.20
fquarter4                          0.52    0.11
depth_sc                          -0.32    0.07
small_cod_density_sc               0.22    0.10
oxygen_sc                          0.22    0.07
flounder_density_sc                0.03    0.07
small_cod_density_sc:oxygen_sc    -0.16    0.08
oxygen_sc:flounder_density_sc      0.00    0.06

Dispersion parameter: 0.10
Tweedie p: 1.54
Matérn range: 14.30
Spatiotemporal IID SD: 0.92
ML criterion at convergence: -5234.112

See ?tidy.sdmTMB to extract these values as a data frame.
distinct: removed 1,582 rows (86%), 265 rows remaining

SAMPLING FOR MODEL 'tmb_generic' NOW (CHAIN 1).
Chain 1: 
Chain 1: Gradient evaluation took 0.005208 seconds
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Chain 1:                215.562 seconds (Total)
Chain 1: 

SAMPLING FOR MODEL 'tmb_generic' NOW (CHAIN 1).
Chain 1: 
Chain 1: Gradient evaluation took 0.004676 seconds
Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 46.76 seconds.
Chain 1: Adjust your expectations accordingly!
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Chain 1: 
filter: removed 4 rows (80%), one row remaining
mutate: new variable 'group' (character) with one unique value and 0% NA
        new variable 'model' (character) with one unique value and 0% NA
filter: removed 3 rows (75%), one row remaining
mutate: new variable 'group' (character) with one unique value and 0% NA
        new variable 'model' (character) with one unique value and 0% NA
mutate: new variable 'year' (double) with one unique value and 0% NA
        new variable 'fyear' (factor) with one unique value and 0% NA
        new variable 'fquarter' (factor) with one unique value and 0% NA
        new variable 'oxygen_sc' (double) with one unique value and 0% NA
        new variable 'depth_sc' (double) with one unique value and 0% NA
        new variable 'small_cod_density_sc' (double) with one unique value and 0% NA
mutate: new variable 'group' (character) with one unique value and 0% NA
        new variable 'xvar' (character) with one unique value and 0% NA
mutate: new variable 'group' (character) with one unique value and 0% NA
        new variable 'xvar' (character) with one unique value and 0% NA
mutate: new variable 'year' (double) with one unique value and 0% NA
        new variable 'fyear' (factor) with one unique value and 0% NA
        new variable 'fquarter' (factor) with one unique value and 0% NA
        new variable 'oxygen_sc' (double) with one unique value and 0% NA
        new variable 'depth_sc' (double) with one unique value and 0% NA
        new variable 'flounder_density_sc' (double) with one unique value and 0% NA
mutate: new variable 'group' (character) with one unique value and 0% NA
        new variable 'xvar' (character) with one unique value and 0% NA
mutate: new variable 'group' (character) with one unique value and 0% NA
        new variable 'xvar' (character) with one unique value and 0% NA
mutate: new variable 'species' (character) with one unique value and 0% NA
        new variable 'response' (character) with one unique value and 0% NA
        new variable 'sig' (character) with 2 unique values and 0% NA
mutate: new variable 'species' (character) with one unique value and 0% NA
        new variable 'response' (character) with one unique value and 0% NA
        new variable 'sig' (character) with 2 unique values and 0% NA
mutate: new variable 'group' (character) with one unique value and 0% NA
mutate: new variable 'group' (character) with one unique value and 0% NA
filter: removed 5,103 rows (57%), 3,851 rows remaining
[1] "flounder"
✔ Non-linear minimizer suggests successful convergence
✔ Hessian matrix is positive definite
✔ No extreme or very small eigenvalues detected
✔ No gradients with respect to fixed effects are >= 0.001
✔ No fixed-effect standard errors are NA
✔ No standard errors look unreasonably large
✔ No sigma parameters are < 0.01
✔ No sigma parameters are > 100
✔ Range parameter doesn't look unreasonably large
Spatiotemporal model fit by ML ['sdmTMB']
Formula: saduria_rel_weight ~ 0 + fyear + fquarter + depth_sc + oxygen_sc + 
 Formula:     small_cod_density_sc * density_saduria_sc + flounder_density_sc * 
 Formula:     density_saduria_sc
Mesh: mesh (isotropic covariance)
Time column: year
Data: dd
Family: tweedie(link = 'log')
 
                                        coef.est coef.se
fyear2015                                  -8.68    1.14
fyear2016                                  -6.46    0.97
fyear2017                                  -8.57    0.97
fyear2018                                  -8.73    1.03
fyear2019                                  -8.42    1.07
fyear2020                                  -8.43    0.97
fyear2021                                 -11.38    1.27
fyear2022                                  -9.19    1.01
fquarter4                                  -0.57    0.21
depth_sc                                   -0.33    0.21
oxygen_sc                                  -0.04    0.22
small_cod_density_sc                        0.41    0.13
density_saduria_sc                          0.25    0.18
flounder_density_sc                        -0.20    0.15
small_cod_density_sc:density_saduria_sc     0.11    0.10
density_saduria_sc:flounder_density_sc     -0.13    0.11

Dispersion parameter: 0.18
Tweedie p: 1.49
Matérn range: 74.50
Spatial SD: 2.20
Spatiotemporal IID SD: 1.59
ML criterion at convergence: -1790.092

See ?tidy.sdmTMB to extract these values as a data frame.
[1] "flounder"
✔ Non-linear minimizer suggests successful convergence
✔ Hessian matrix is positive definite
✔ No extreme or very small eigenvalues detected
✔ No gradients with respect to fixed effects are >= 0.001
✔ No fixed-effect standard errors are NA
✔ No standard errors look unreasonably large
✔ No sigma parameters are < 0.01
✔ No sigma parameters are > 100
✔ Range parameter doesn't look unreasonably large
Spatiotemporal model fit by ML ['sdmTMB']
Formula: benthic_rel_weight ~ 0 + fyear + fquarter + depth_sc + small_cod_density_sc * 
 Formula:     oxygen_sc + flounder_density_sc * oxygen_sc
Mesh: mesh (isotropic covariance)
Time column: year
Data: dd
Family: tweedie(link = 'log')
 
                               coef.est coef.se
fyear2015                         -5.11    0.31
fyear2016                         -4.94    0.24
fyear2017                         -4.98    0.20
fyear2018                         -5.50    0.24
fyear2019                         -5.17    0.26
fyear2020                         -4.70    0.19
fyear2021                         -5.34    0.25
fyear2022                         -5.03    0.21
fquarter4                          0.04    0.10
depth_sc                          -0.36    0.10
small_cod_density_sc               0.22    0.06
oxygen_sc                         -0.05    0.07
flounder_density_sc               -0.03    0.07
small_cod_density_sc:oxygen_sc     0.00    0.03
oxygen_sc:flounder_density_sc     -0.02    0.05

Dispersion parameter: 0.17
Tweedie p: 1.50
Matérn range: 18.38
Spatial SD: 0.95
Spatiotemporal IID SD: 0.67
ML criterion at convergence: -5535.441

See ?tidy.sdmTMB to extract these values as a data frame.
distinct: removed 3,590 rows (93%), 261 rows remaining

SAMPLING FOR MODEL 'tmb_generic' NOW (CHAIN 1).
Chain 1: 
Chain 1: Gradient evaluation took 0.005659 seconds
Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 56.59 seconds.
Chain 1: Adjust your expectations accordingly!
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Chain 1:                291.368 seconds (Total)
Chain 1: 

SAMPLING FOR MODEL 'tmb_generic' NOW (CHAIN 1).
Chain 1: 
Chain 1: Gradient evaluation took 0.005409 seconds
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Chain 1: Adjust your expectations accordingly!
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Chain 1: 
filter: removed 4 rows (80%), one row remaining
mutate: new variable 'group' (character) with one unique value and 0% NA
        new variable 'model' (character) with one unique value and 0% NA
filter: removed 4 rows (80%), one row remaining
mutate: new variable 'group' (character) with one unique value and 0% NA
        new variable 'model' (character) with one unique value and 0% NA
mutate: new variable 'year' (double) with one unique value and 0% NA
        new variable 'fyear' (factor) with one unique value and 0% NA
        new variable 'fquarter' (factor) with one unique value and 0% NA
        new variable 'oxygen_sc' (double) with one unique value and 0% NA
        new variable 'depth_sc' (double) with one unique value and 0% NA
        new variable 'small_cod_density_sc' (double) with one unique value and 0% NA
mutate: new variable 'group' (character) with one unique value and 0% NA
        new variable 'xvar' (character) with one unique value and 0% NA
mutate: new variable 'group' (character) with one unique value and 0% NA
        new variable 'xvar' (character) with one unique value and 0% NA
mutate: new variable 'year' (double) with one unique value and 0% NA
        new variable 'fyear' (factor) with one unique value and 0% NA
        new variable 'fquarter' (factor) with one unique value and 0% NA
        new variable 'oxygen_sc' (double) with one unique value and 0% NA
        new variable 'depth_sc' (double) with one unique value and 0% NA
        new variable 'flounder_density_sc' (double) with one unique value and 0% NA
mutate: new variable 'group' (character) with one unique value and 0% NA
        new variable 'xvar' (character) with one unique value and 0% NA
mutate: new variable 'group' (character) with one unique value and 0% NA
        new variable 'xvar' (character) with one unique value and 0% NA
mutate: new variable 'species' (character) with one unique value and 0% NA
        new variable 'response' (character) with one unique value and 0% NA
        new variable 'sig' (character) with 2 unique values and 0% NA
mutate: new variable 'species' (character) with one unique value and 0% NA
        new variable 'response' (character) with one unique value and 0% NA
        new variable 'sig' (character) with 2 unique values and 0% NA
mutate: new variable 'group' (character) with one unique value and 0% NA
mutate: new variable 'group' (character) with one unique value and 0% NA

Now do a separate model for adult cod looking at total prey

  dd <- filter(d, group == "large cod")
filter: removed 5,698 rows (64%), 3,256 rows remaining
  mesh <- make_mesh(dd,
                    xy_cols = c("X", "Y"),
                    cutoff = 5)

  # Total model
  # NOTE: turning off spatial here due to convergence and AIC
  m_tot <- sdmTMB(tot_rel_weight ~ 0 + fyear + fquarter + depth_sc + 
                    large_cod_density_sc*oxygen_sc + flounder_density_sc*oxygen_sc,
                  data = dd,
                  mesh = mesh,
                  family = tweedie(),
                  spatiotemporal = "IID", 
                  spatial = "off",
                  time = "year")
  
  sanity(m_tot)
✔ Non-linear minimizer suggests successful convergence
✔ Hessian matrix is positive definite
✔ No extreme or very small eigenvalues detected
✔ No gradients with respect to fixed effects are >= 0.001
✔ No fixed-effect standard errors are NA
✔ No standard errors look unreasonably large
✔ No sigma parameters are < 0.01
✔ No sigma parameters are > 100
✔ Range parameter doesn't look unreasonably large
  print(m_tot)
Spatiotemporal model fit by ML ['sdmTMB']
Formula: tot_rel_weight ~ 0 + fyear + fquarter + depth_sc + large_cod_density_sc * 
 Formula:     oxygen_sc + flounder_density_sc * oxygen_sc
Mesh: mesh (isotropic covariance)
Time column: year
Data: dd
Family: tweedie(link = 'log')
 
                               coef.est coef.se
fyear2015                         -4.15    0.21
fyear2016                         -4.64    0.16
fyear2017                         -4.53    0.13
fyear2018                         -4.34    0.15
fyear2019                         -4.76    0.22
fyear2020                         -4.59    0.13
fyear2021                         -4.36    0.13
fyear2022                         -4.61    0.15
fquarter4                         -0.19    0.10
depth_sc                          -0.01    0.05
large_cod_density_sc               0.16    0.06
oxygen_sc                         -0.03    0.05
flounder_density_sc               -0.01    0.05
large_cod_density_sc:oxygen_sc     0.11    0.05
oxygen_sc:flounder_density_sc     -0.09    0.04

Dispersion parameter: 0.60
Tweedie p: 1.71
Matérn range: 14.87
Spatiotemporal IID SD: 0.62
ML criterion at convergence: -7359.392

See ?tidy.sdmTMB to extract these values as a data frame.
  # Residuals
  samps <- sdmTMBextra::predict_mle_mcmc(m_tot, mcmc_iter = 401, mcmc_warmup = 400)

SAMPLING FOR MODEL 'tmb_generic' NOW (CHAIN 1).
Chain 1: 
Chain 1: Gradient evaluation took 0.004329 seconds
Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 43.29 seconds.
Chain 1: Adjust your expectations accordingly!
Chain 1: 
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Chain 1: 
Chain 1:  Elapsed Time: 26.061 seconds (Warm-up)
Chain 1:                0.08 seconds (Sampling)
Chain 1:                26.141 seconds (Total)
Chain 1: 
  mcmc_res <- residuals(m_tot, type = "mle-mcmc", mcmc_samples = samps)
  dd$res <- as.vector(mcmc_res)
    
  res_tot <- dd
  
  # Range
  range_tot <- tidy(m_tot, effects = "ran_pars") %>% filter(term == "range") %>% mutate(group = "large cod", model = "total")
filter: removed 3 rows (75%), one row remaining
mutate: new variable 'group' (character) with one unique value and 0% NA
        new variable 'model' (character) with one unique value and 0% NA
  # Spatial and spatiotemporal random effects
  d_haul <- dd %>% 
    distinct(haul_id, .keep_all = TRUE)
distinct: removed 2,968 rows (91%), 288 rows remaining
  preds_tot <- predict(m_tot, newdata = d_haul)
  
  # Coefficients
  coefs_tot <- bind_rows(tidy(m_tot, effects = "fixed", conf.int = TRUE)) %>% 
    mutate(species = "Cod (m)",
           response = "Saduria",
           sig = ifelse(estimate > 0 & conf.low > 0, "Y", "N"),
           sig = ifelse(estimate < 0 & conf.high < 0, "Y", sig))
mutate: new variable 'species' (character) with one unique value and 0% NA
        new variable 'response' (character) with one unique value and 0% NA
        new variable 'sig' (character) with 2 unique values and 0% NA
  coefs_tot <- coefs_tot %>% mutate(group = "large cod")
mutate: new variable 'group' (character) with one unique value and 0% NA
  # Conditional effects: flounder
  nd_flounder <- data.frame(expand_grid(
    flounder_density_sc = seq(quantile(dd$flounder_density_sc, probs = 0.05),
                              quantile(dd$flounder_density_sc, probs = 0.95),
                              length.out = 50))) %>%
    mutate(year = 2020,
           fyear = as.factor(2020),
           fquarter = as.factor(1),
           oxygen_sc = 0,
           depth_sc = 0,
           large_cod_density_sc = 0)
mutate: new variable 'year' (double) with one unique value and 0% NA
        new variable 'fyear' (factor) with one unique value and 0% NA
        new variable 'fquarter' (factor) with one unique value and 0% NA
        new variable 'oxygen_sc' (double) with one unique value and 0% NA
        new variable 'depth_sc' (double) with one unique value and 0% NA
        new variable 'large_cod_density_sc' (double) with one unique value and 0% NA
  preds_flounder_tot <- predict(m_tot, newdata = nd_flounder, re_form = NA, re_form_iid = NA, se_fit = TRUE)
  pred_flounder_tot <- preds_flounder_tot %>% mutate(group = "large cod", xvar = "flounder")
mutate: new variable 'group' (character) with one unique value and 0% NA
        new variable 'xvar' (character) with one unique value and 0% NA

Make dataframes

coef_df <- bind_rows(bind_rows(coef_sad) %>% mutate(model = "Saduria"),
                     bind_rows(coef_ben) %>% mutate(model = "Benthos"))
mutate: new variable 'model' (character) with one unique value and 0% NA
mutate: new variable 'model' (character) with one unique value and 0% NA
coef_df <- coef_df %>% bind_rows(coefs_tot %>% mutate(model = "Total"))
mutate: new variable 'model' (character) with one unique value and 0% NA
pred_cod_df <- bind_rows(bind_rows(pred_cod_sad) %>% mutate(model = "Saduria"),
                         bind_rows(pred_cod_ben) %>% mutate(model = "Benthos"))
mutate: new variable 'model' (character) with one unique value and 0% NA
mutate: new variable 'model' (character) with one unique value and 0% NA
pred_flounder_df <- bind_rows(bind_rows(pred_flounder_sad) %>% mutate(model = "Saduria"),
                              bind_rows(pred_flounder_ben) %>% mutate(model = "Benthos"))
mutate: new variable 'model' (character) with one unique value and 0% NA
mutate: new variable 'model' (character) with one unique value and 0% NA
res_df <- bind_rows(bind_rows(res_sad) %>% mutate(model = "Saduria"),
                    bind_rows(res_ben) %>% mutate(model = "Benthos"))
mutate: new variable 'model' (character) with one unique value and 0% NA
mutate: new variable 'model' (character) with one unique value and 0% NA
res_df <- res_df %>% bind_rows(res_tot %>% mutate(model = "Total"))
mutate: new variable 'model' (character) with one unique value and 0% NA
random_df <- bind_rows(bind_rows(random_sad) %>% mutate(model = "Saduria"),
                       bind_rows(random_ben) %>% mutate(model = "Benthos"))
mutate: new variable 'model' (character) with one unique value and 0% NA
mutate: new variable 'model' (character) with one unique value and 0% NA
random_df <- random_df %>% bind_rows(preds_tot %>% mutate(model = "Total"))
mutate: new variable 'model' (character) with one unique value and 0% NA
range_df <- bind_rows(range_tot, bind_rows(range_ben), bind_rows(range_sad))

Plot spatial random effects

random_df <- random_df %>%
  mutate(group = str_to_sentence(group))
mutate: changed 1,916 values (100%) of 'group' (0 new NA)
# Saduria
plot_map_fc +
  geom_point(data = random_df %>% filter(model == "Saduria"),
             aes(X*1000, Y*1000, color = omega_s), size = 0.9) +
  scale_color_gradient2() +
  facet_wrap(~factor(group, levels = c("Flounder", "Small cod", "Large cod"))) +
  labs(color = "Spatial\nrandom effect") +
  theme(axis.text.x = element_text(angle = 90),
        legend.position = "bottom",
        #legend.direction = "vertical",
        legend.key.width = unit(0.6, "cm"),
        legend.key.height = unit(0.2, "cm"))
filter: removed 1,102 rows (58%), 814 rows remaining

ggsave(paste0(home, "/figures/supp/omega_sad.pdf"), width = 17, height = 9, units = "cm")


# Now do benthos (only for flounder)
plot_map_fc +
  geom_point(data = random_df %>% filter(model == "Benthos" & group == "Flounder"),
             aes(X*1000, Y*1000, color = omega_s), size = 0.9) +
  scale_color_gradient2() +
  facet_wrap(~ group) +
  labs(color = "Spatial\nrandom effect") +
  theme(axis.text.x = element_text(angle = 90),
        legend.position = "right",
        legend.direction = "vertical",
        legend.key.width = unit(0.4, "cm"),
        legend.key.height = unit(0.4, "cm"))
filter: removed 1,655 rows (86%), 261 rows remaining

ggsave(paste0(home, "/figures/supp/omega_ben.pdf"), width = 11, height = 11, units = "cm")

Plot spatiotemporal random effects

# Saduria
sad_eps_sc <- plot_map_fc +
  geom_point(data = random_df %>% filter(model == "Saduria" & group == "Small cod"), aes(X*1000, Y*1000, color = epsilon_st), size = 0.9) +
  scale_color_gradient2() +
  facet_wrap(~year) +
  labs(color = "Spatiotemporal\nrandom effect") +
  theme(legend.position = c(0.84, 0.16),
        axis.text.x = element_text(angle = 90))
filter: removed 1,651 rows (86%), 265 rows remaining
Warning: A numeric `legend.position` argument in `theme()` was deprecated in ggplot2
3.5.0.
ℹ Please use the `legend.position.inside` argument of `theme()` instead.
sad_eps_sc

ggsave(paste0(home, "/figures/supp/epsilon_sad_small_cod.pdf"), width = 17, height = 17, units = "cm")

sad_eps_lc <- plot_map_fc +
  geom_point(data = random_df %>% filter(model == "Saduria" & group == "Large cod"), aes(X*1000, Y*1000, color = epsilon_st), size = 0.9) +
  scale_color_gradient2() +
  facet_wrap(~ year) +
  labs(color = "Spatiotemporal\nrandom effect") +
  theme(legend.position = c(0.84, 0.16),
        axis.text.x = element_text(angle = 90))
filter: removed 1,628 rows (85%), 288 rows remaining
sad_eps_lc

ggsave(paste0(home, "/figures/supp/epsilon_sad_large_cod.pdf"), width = 17, height = 17, units = "cm")

sad_eps_f <- plot_map_fc +
  geom_point(data = random_df %>% filter(model == "Saduria" & group == "Flounder"), aes(X*1000, Y*1000, color = epsilon_st), size = 0.9) +
  scale_color_gradient2() +
  facet_wrap(~ year) +
  labs(color = "Spatiotemporal\nrandom effect") +
  theme(legend.position = c(0.84, 0.16),
        axis.text.x = element_text(angle = 90))
filter: removed 1,655 rows (86%), 261 rows remaining
sad_eps_f

ggsave(paste0(home, "/figures/supp/epsilon_sad_flounder.pdf"), width = 17, height = 17, units = "cm")


# Benthos
ben_eps_sc <- plot_map_fc +
  geom_point(data = random_df %>% filter(model == "Benthos" & group == "Small cod"), aes(X*1000, Y*1000, color = epsilon_st), size = 0.9) +
  scale_color_gradient2() +
  facet_wrap(~ year) +
  labs(color = "Spatiotemporal\nrandom effect") +
  theme(legend.position = c(0.84, 0.16),
        axis.text.x = element_text(angle = 90))
filter: removed 1,651 rows (86%), 265 rows remaining
ben_eps_sc

ggsave(paste0(home, "/figures/supp/epsilon_ben_small_cod.pdf"), width = 17, height = 17, units = "cm")

ben_eps_lc <- plot_map_fc +
  geom_point(data = random_df %>% filter(model == "Benthos" & group == "Large cod"), aes(X*1000, Y*1000, color = epsilon_st), size = 0.9) +
  scale_color_gradient2() +
  facet_wrap(~ year) +
  labs(color = "Spatiotemporal\nrandom effect") +
  theme(legend.position = c(0.84, 0.16),
        axis.text.x = element_text(angle = 90))
filter: removed 1,628 rows (85%), 288 rows remaining
ben_eps_lc

ggsave(paste0(home, "/figures/supp/epsilon_ben_large_cod.pdf"), width = 17, height = 17, units = "cm")

ben_eps_f <- plot_map_fc +
  geom_point(data = random_df %>% filter(model == "Benthos" & group == "Flounder"), aes(X*1000, Y*1000, color = epsilon_st), size = 0.9) +
  scale_color_gradient2() +
  facet_wrap(~ year) +
  labs(color = "Spatiotemporal\nrandom effect") +
  theme(legend.position = c(0.84, 0.16),
        axis.text.x = element_text(angle = 90))
filter: removed 1,655 rows (86%), 261 rows remaining
ben_eps_f

ggsave(paste0(home, "/figures/supp/epsilon_ben_flounder.pdf"), width = 17, height = 17, units = "cm")


# Total
tot_eps <- plot_map_fc + 
    geom_point(data = preds_tot, aes(X*1000, Y*1000, color = epsilon_st), size = 0.9) + 
    scale_color_gradient2() +
    facet_wrap(~ year) +
    labs(color = "Spatiotemporal\nrandom effect") +
    theme(legend.position = c(0.84, 0.16),
          axis.text.x = element_text(angle = 90))

tot_eps

Plot range

#pal <- brewer.pal(n = 8, name = "Dark2")[c(2, 7, 6)]
pal <- (brewer.pal(n = 11, name = "RdYlBu")[c(11, 4, 1)])

range_df %>% arrange(estimate)
# A tibble: 7 × 5
  term  estimate std.error group     model  
  <chr>    <dbl>     <dbl> <chr>     <chr>  
1 range     9.20      2.79 large cod benthos
2 range    14.3       4.14 small cod benthos
3 range    14.9       4.88 large cod total  
4 range    18.4       4.36 flounder  benthos
5 range    34.1      16.2  large cod saduria
6 range    65.6      30.1  small cod saduria
7 range    74.5      16.6  flounder  saduria
range_df %>% 
  mutate(group = str_to_sentence(group),
         model2 = ifelse(model == "benthos", "Benthic prey", model),
         model2 = ifelse(model == "saduria", "Saduria", model2),
         model2 = ifelse(model == "total", "Total prey", model2)) %>% 
  ggplot(aes(model2, estimate, color = factor(group, levels = c("Flounder", "Small cod", "Large cod")))) + 
  geom_point(size = 2) +
  geom_hline(yintercept = 5, linetype = 2, alpha = 0.5) +
  scale_color_manual(values = pal) + 
  labs(x = "", y = "Range (km)", color = "Predator") + 
  theme(aspect.ratio = 1,
        legend.position = c(0.86, 0.86)) 
mutate: changed 7 values (100%) of 'group' (0 new NA)
        new variable 'model2' (character) with 3 unique values and 0% NA

ggsave(paste0(home, "/figures/supp/ranges.pdf"), width = 11, height = 11, units = "cm")

Plot residuals

# Plot residuals
res_df %>% 
  mutate(group = str_to_title(group)) %>% 
  ggplot(aes(sample = res)) +
  stat_qq(size = 0.75, shape = 21, fill = NA) +
  facet_grid(model ~ group) +
  stat_qq_line() +
  labs(y = "Sample Quantiles", x = "Theoretical Quantiles") +
  theme(aspect.ratio = 1)
mutate: changed 21,164 values (100%) of 'group' (0 new NA)

ggsave(paste0(home, "/figures/supp/qq_relative_prey_weight.pdf"), width = 17, height = 17, units = "cm")

Plot coefficients

coef_df$term %>% unique()
 [1] "fyear2015"                              
 [2] "fyear2016"                              
 [3] "fyear2017"                              
 [4] "fyear2018"                              
 [5] "fyear2019"                              
 [6] "fyear2020"                              
 [7] "fyear2021"                              
 [8] "fyear2022"                              
 [9] "fquarter4"                              
[10] "depth_sc"                               
[11] "oxygen_sc"                              
[12] "small_cod_density_sc"                   
[13] "density_saduria_sc"                     
[14] "flounder_density_sc"                    
[15] "small_cod_density_sc:density_saduria_sc"
[16] "density_saduria_sc:flounder_density_sc" 
[17] "small_cod_density_sc:oxygen_sc"         
[18] "oxygen_sc:flounder_density_sc"          
[19] "large_cod_density_sc"                   
[20] "large_cod_density_sc:oxygen_sc"         
# Fix some names
coef_df2 <- coef_df %>%
  filter(!grepl('year', term)) %>%
  filter(!grepl('quarter', term)) %>%
  mutate(term = str_remove_all(term, "_sc"),
         term = str_remove_all(term, "density"),
         term = str_replace_all(term, "_", ""),
         term = str_replace_all(term, "geco", "ge co"),
         term = str_replace_all(term, "llco", "ll co"),
         term = str_replace(term, ":", " × "),
         term = str_to_sentence(term),
         group = str_to_sentence(group)) %>% 
  mutate(model2 = ifelse(model == "Saduria", "Prey=Saduria", NA),
         model2 = ifelse(model == "Benthos", "Prey=Benthic prey", model2),
         model2 = ifelse(model == "Total", "Prey=Total prey", model2)) %>% 
  mutate(sig2 = ifelse(sig == "Y", "N", "Y"))
filter: removed 56 rows (52%), 52 rows remaining
filter: removed 7 rows (13%), 45 rows remaining
mutate: changed 45 values (100%) of 'term' (0 new NA)
        changed 45 values (100%) of 'group' (0 new NA)
mutate: new variable 'model2' (character) with 3 unique values and 0% NA
mutate: new variable 'sig2' (character) with 2 unique values and 0% NA
p1 <- 
  coef_df2 %>% 
  filter(model == "Benthos") %>% 
  ggplot(aes(estimate, term, alpha = sig2,
                 color = factor(group, levels = c("Flounder", "Small cod", "Large cod")))) +
  geom_stripped_rows(aes(y = term), inherit.aes = FALSE) +
  facet_wrap2(~model2, ncol = 2, scales = "free") +
  geom_vline(xintercept = 0, linetype = 2, alpha = 0.5, color = "gray10", linewidth = 0.2) +
  geom_point(position = position_dodge(width = 0.5), size = 1.5) +
  geom_errorbar(aes(xmin = conf.low, xmax = conf.high), width = 0,
                position = position_dodge(width = 0.5)) +
  scale_alpha_manual(values = c(1, 0.4)) +
  scale_color_manual(values = pal) +
  labs(x = "", y = "", alpha = "95% CI crossing 0", color = "Predator") +
  guides(color = guide_legend(title.position = "top", title.hjust = 0.5),
         alpha = guide_legend(title.position = "top", title.hjust = 0.5)) +
  theme(legend.position = c(0.75, 0.2),
        legend.direction = "vertical",
        legend.box.spacing = unit(-3, "pt"),
        legend.margin = margin(0, 0, 0, 0)) +
  NULL
filter: removed 27 rows (60%), 18 rows remaining
p2 <- 
  coef_df2 %>% 
  filter(model == "Saduria") %>% 
  ggplot(aes(estimate, term, alpha = sig2,
                 color = factor(group, levels = c("Flounder", "Small cod", "Large cod")))) +
  geom_stripped_rows(aes(y = term), inherit.aes = FALSE) +
  facet_wrap2(~model2, ncol = 2, scales = "free") +
  geom_vline(xintercept = 0, linetype = 2, alpha = 0.5, color = "gray10", linewidth = 0.2) +
  geom_point(position = position_dodge(width = 0.5), size = 1.5) +
  geom_errorbar(aes(xmin = conf.low, xmax = conf.high), width = 0,
                position = position_dodge(width = 0.5)) +
  scale_alpha_manual(values = c(1, 0.4)) +
  scale_color_manual(values = pal) +
  labs(x = "", y = "") +
  guides(color = "none",
         alpha = "none")
filter: removed 24 rows (53%), 21 rows remaining
p3 <- 
  coef_df2 %>% 
  filter(model == "Total") %>% 
  ggplot(aes(estimate, term, alpha = sig2,
                 color = "Large cod")) +
  geom_stripped_rows(aes(y = term), inherit.aes = FALSE) +
  facet_wrap2(~model2, ncol = 2, scales = "free") +
  geom_vline(xintercept = 0, linetype = 2, alpha = 0.5, color = "gray10", linewidth = 0.2) +
  geom_point(position = position_dodge(width = 0.5), size = 1.5) +
  geom_errorbar(aes(xmin = conf.low, xmax = conf.high), width = 0,
                position = position_dodge(width = 0.5)) +
  scale_alpha_manual(values = c(1, 0.4)) +
  scale_color_manual(values = pal[3]) +
  labs(x = "", y = "") +
  guides(color = "none",
         alpha = "none")
filter: removed 39 rows (87%), 6 rows remaining
p2 / p1 / p3 +
  plot_annotation(tag_levels = "a") +
  plot_layout(axes = "collect", guides = "collect") & 
  theme(legend.position = "bottom") &
  coord_cartesian(xlim = c(-1.55, 1.15))

ggsave(paste0(home, "/figures/coefs.pdf"), width = 11, height = 22, units = "cm")

Plot year and quarter coefficients

# Fix some names
coef_df3 <- coef_df %>%
  filter(grepl('year', term)) %>%
  mutate(term = str_remove_all(term, "fyear"),
         group = str_to_sentence(group),
         term = as.numeric(term),
         model2 = ifelse(model == "Benthos", "Benthic prey", model),
         model2 = ifelse(model == "Saduria", "Saduria", model2),
         model2 = ifelse(model == "Total", "Total prey", model2))
filter: removed 52 rows (48%), 56 rows remaining
mutate: converted 'term' from character to double (0 new NA)
        changed 56 values (100%) of 'group' (0 new NA)
        new variable 'model2' (character) with 3 unique values and 0% NA
ggplot(coef_df3, aes(term, exp(estimate), color = factor(group, levels = c("Flounder", "Small cod", "Large cod")), 
                     fill = factor(group, levels = c("Flounder", "Small cod", "Large cod")))) +
  facet_wrap(~model2, scales = "free", ncol = 1) +
  #geom_line(position = position_dodge(width = 0.5)) +
  geom_point(position = position_dodge(width = 0.4)) +
  #geom_ribbon(aes(ymin = exp(conf.low), ymax = exp(conf.high)), alpha = 0.2, color = NA) +
  geom_errorbar(aes(ymin = exp(conf.low), ymax = exp(conf.high)), alpha = 0.4, width = 0,
                position = position_dodge(width = 0.4)) +
  scale_color_manual(values = pal) +
  scale_fill_manual(values = pal) +
  labs(x = "Year", y = "Standardized coefficient", color = "") +
  guides(color = guide_legend(title.position = "top", title.hjust = 0.5, ncol = 3),
         fill = "none") +
  theme(legend.position = c(0.5, 0.99),
        legend.direction = "vertical",
        legend.box.spacing = unit(-3, "pt"),
        legend.margin = margin(0, 0, 0, 0),
        strip.text.x.top = element_text(angle = 0, hjust = 0)) +
  NULL

ggsave(paste0(home, "/figures/supp/coefs_year.pdf"), width = 11, height = 21, units = "cm")
# Now do quarter
coef_df5 <- coef_df %>%
  filter(term %in% c("fquarter4")) %>% 
  mutate(group = str_to_sentence(group),
         model2 = ifelse(model == "Benthos", "Benthic prey", model),
         model2 = ifelse(model == "Saduria", "Saduria", model2),
         model2 = ifelse(model == "Total", "Total prey", model2)) %>% 
  mutate(sig2 = ifelse(sig == "Y", "N", "Y"))
filter: removed 101 rows (94%), 7 rows remaining
mutate: changed 7 values (100%) of 'group' (0 new NA)
        new variable 'model2' (character) with 3 unique values and 0% NA
mutate: new variable 'sig2' (character) with 2 unique values and 0% NA
ggplot(coef_df5, aes(estimate, model2,
                     alpha = sig2,
                     color = factor(group, levels = c("Flounder", "Small cod", "Large cod")))) +
  geom_vline(xintercept = 0, linetype = 2, alpha = 0.5, color = "gray10", linewidth = 0.2) +
  geom_point(position = position_dodge(width = 0.5), size = 1.5) +
  geom_errorbar(aes(xmin = conf.low, xmax = conf.high), width = 0,
                position = position_dodge(width = 0.5)) +
  scale_alpha_manual(values = c(1, 0.4)) +
  scale_color_manual(values = pal) +
  labs(x = "", y = "Quarter 4 effect", alpha = "95% CI crossing 0", color = "Predator") +
  guides(color = guide_legend(title.position = "top", title.hjust = 0.5),
         alpha = guide_legend(title.position = "top", title.hjust = 0.5)) +
  geom_stripped_rows(aes(y = model2), inherit.aes = FALSE) +
  theme(legend.position = "bottom",
        legend.direction = "horizontal",
        legend.box = "horizontal",
        legend.box.spacing = unit(-3, "pt"),
        legend.margin = margin(0, 0, 0, 0)) + 
  coord_cartesian(expand = 0)

ggsave(paste0(home, "/figures/supp/coefs_quarter.pdf"), width = 17, height = 11, units = "cm")

Conditional effects

# Which CI?
# https://www.calculator.net/confidence-interval-calculator.html
pred_df <- bind_rows(pred_cod_df, pred_flounder_df) %>%
  mutate(group = str_to_sentence(group),
         sad = ifelse(density_saduria_sc == min(density_saduria_sc), "Low", NA),
         sad = ifelse(density_saduria_sc == max(density_saduria_sc), "High", sad)) %>% 
  drop_na(sad)
mutate: changed 1,500 values (100%) of 'group' (0 new NA)
        new variable 'sad' (character) with 3 unique values and 20% NA
drop_na: removed 300 rows (20%), 1,200 rows remaining
pred_df2 <- bind_rows(pred_flounder_df,
                      pred_flounder_tot %>% mutate(model = "Total")) %>% 
  mutate(group = str_to_sentence(group),
         density_saduria_sc = replace_na(density_saduria_sc,
                                         median(density_saduria_sc, na.rm = TRUE)))
mutate: new variable 'model' (character) with one unique value and 0% NA
mutate: changed 50 values (5%) of 'density_saduria_sc' (50 fewer NA)
        changed 950 values (100%) of 'group' (0 new NA)
# 75% CI!!
ggplot(pred_df %>% filter(model == "Saduria" & xvar == "flounder"),# & !group == "Large cod"),
       aes(flounder_density_sc, exp(est), color = sad, fill = sad)) +
  geom_ribbon(aes(ymin = exp(est - 1.150*est_se), ymax = exp(est + 1.150*est_se)),
              alpha = 0.3, color = NA) +
  geom_line() +
  facet_wrap(~factor(group, levels = c("Flounder", "Small cod", "Large cod")),
             scales = "free", 
             ncol = 3) +
  scale_color_brewer(palette = "Dark2") +
  scale_fill_brewer(palette = "Dark2") +
  coord_cartesian(#xlim = c(-0.5, 0.5), 
                  expand = 0, clip = "off") +
  labs(x = "Flounder density", y = "Relative saduria weight",
       color = "Saduria", fill = "Saduria") + 
  theme(legend.position = c(0.95, 0.84),
        strip.text.x.top = element_text(angle = 0, hjust = 0)) + 
  scale_x_continuous(breaks = c(-1, 0, 1)) +
  NULL
filter: removed 900 rows (75%), 300 rows remaining

ggsave(paste0(home, "/figures/conditional_saduria_flounder.pdf"), width = 19, height = 7, units = "cm")

Showing conditional effects of oxygen on small cod feeding on benthos

  dd <- filter(d, group == "small cod")
filter: removed 7,107 rows (79%), 1,847 rows remaining
  mesh <- make_mesh(dd,
                    xy_cols = c("X", "Y"),
                    cutoff = 5)

  # Benthic model
  m_ben <- sdmTMB(benthic_rel_weight ~ 0 + fyear + fquarter + depth_sc + 
                    small_cod_density_sc*oxygen_sc + flounder_density_sc*oxygen_sc,
                  data = dd,
                  mesh = mesh,
                  family = tweedie(),
                  spatiotemporal = "IID",
                  spatial = "off",
                  time = "year")

  sanity(m_ben)
✔ Non-linear minimizer suggests successful convergence
✔ Hessian matrix is positive definite
✔ No extreme or very small eigenvalues detected
✔ No gradients with respect to fixed effects are >= 0.001
✔ No fixed-effect standard errors are NA
✔ No standard errors look unreasonably large
✔ No sigma parameters are < 0.01
✔ No sigma parameters are > 100
✔ Range parameter doesn't look unreasonably large
  nd <- data.frame(oxygen = seq(quantile(d$oxygen, probs = 0.05), quantile(d$oxygen, probs = 0.95),
                                length.out = 50)) %>%
    mutate(year = 2020,
           fyear = as.factor(2020),
           fquarter = as.factor(1),
           density_saduria_sc = 0,
           flounder_density_sc = 0,
           depth_sc = 0,
           small_cod_density_sc = 0) %>%
    mutate(oxygen_sc = (oxygen - mean(d$oxygen)) / sd(d$oxygen))
mutate: new variable 'year' (double) with one unique value and 0% NA
        new variable 'fyear' (factor) with one unique value and 0% NA
        new variable 'fquarter' (factor) with one unique value and 0% NA
        new variable 'density_saduria_sc' (double) with one unique value and 0% NA
        new variable 'flounder_density_sc' (double) with one unique value and 0% NA
        new variable 'depth_sc' (double) with one unique value and 0% NA
        new variable 'small_cod_density_sc' (double) with one unique value and 0% NA
mutate: new variable 'oxygen_sc' (double) with 50 unique values and 0% NA
  p <- predict(m_ben, newdata = nd, re_form = NA, re_form_iid = NA, se_fit = TRUE)

  ggplot(p, aes(oxygen, exp(est))) +
    geom_line() +
    theme_sleek(base_size = 14) +
    geom_hline(yintercept = 0.0025, col = "red") +
    geom_hline(yintercept = 0.0040, col = "red") +
    geom_vline(xintercept = 4.8, col = "red") +
    geom_vline(xintercept = 7.6, col = "red") +
    NULL